# Remaining fuel estimation/measuring Strategy in a spacecraft

During descent of a spacecraft to any planetary body the spacecraft uses retro engine with variable throttle to reduce the vehicle velocity to zero at touchdown.

Inorder to compute for the amount of throttle required the guidance needs mass and inertia(for RCS) of the spacecraft.

However, the mass and inertia are changing constantly as fuel is being used. It is definitely possible to compute onboard how much fuel is remaining based on throttle history. But this will result in error accumulation over time and probably the margins of closed loop controller will be exhausted.

So my question is... do spacecrafts employ some fuel measuring device on board? Like the way cars do ! However same device principle will obviously not work.

• I would have assume a flowmeter to know how many propellant has been used (and deduce the remaining fuel) – Manu H Jun 17 '19 at 6:25
• Measuring liquid fuel amounts is difficult in zero gravity. But measuring pressure for gaseous cold gas thrusters is easy in comparison. – Uwe Jun 18 '19 at 14:06

In order to compute for the amount of throttle required the guidance needs mass and inertia (for RCS) of the spacecraft.

What's actually important is to know your position, velocity, and acceleration. Estimates of mass are obviously useful but don't have to be 100% accurate if you have closed-loop control and good knowledge of your current acceleration.

For position and velocity, you'll want something like a radar altimeter and/or GPS.

An on-board accelerometer takes care of any errors in either the mass or thrust estimate, and automatically incorporates any atmospheric effects if you're landing on a body with an atmosphere.

Direct measurement of propellant level would be subject to errors due to sloshing; it's possible that dead-reckoning estimates of prop levels based on flow rate would be more accurate.

Measure of propellant level in zero-gee tankage is a tricky problem.

Shuttle attempted it in its Orbital Manuevering System.

A capacitance gauging system in each OMS propellant tank measures the propellant in the tank. The system consists of a forward and aft probe and a totalizer. The forward and aft fuel probes use fuel (which is a conductor) as one plate of the capacitor and a glass tube that is metallized on the inside as the other. The forward and aft oxidizer probes use two concentric nickel tubes as the capacitor plates and oxidizer as the dielectric. (Helium is also a dielectric, but has a different dielectric constant than the oxidizer.) The aft probes in each tank contain a resistive temperature-sensing element to correct variations in fluid density. The fluid in the area of the communication screens cannot be measured.

The system was problematic and Orbiters often flew with it nonfunctional.

The Orbiter's Reaction Control System tanks used algorithmic gauging

The RCS quantity monitor uses the GPC to calculate the usable percent of fuel and oxidizer in each RCS module. The quantities are computed based on the pressure, volume, and temperature method, which requires that pressure and temperature measurements be combined with a unique set of constants to calculate the percent remaining in each of the six propellant tanks. Correction factors are included for residual tank propellant at depletion, gauging inaccuracy, and trapped line propellant. The computed quantity represents the usable (rather than total) quantity for each module and makes it possible to determine if the difference between each pair of tanks exceeds a preset tolerance (leak detection). The sequence assumes that helium flows to the propellant tanks to replace propellant leaving. As a result, the computed quantity remaining in a propellant tank will be decreased by normal usage, propellant leaks, or helium leaks.

(GPC = General Purpose Computer)

Propellant transferred between the two systems was estimated by a burn-time algorithm.

Reference 1

Just for completeness, the shuttle's External Tank didn't have a sophisticated gauging system for its propellant. Instead, simple on/off level sensors were used to aid in filling the tank, and to shut off the engines if the tank ran dry prematurely.

Reference 2

• Thanks ! Exactly what I was looking for. But it seems interplanetary landers dont employ any such technique. – Prakhar Apr 24 '18 at 1:00
• It's possible the used some variant of the algorithmic gauging approach. The tank-probe approach didn't work very well. – Organic Marble Apr 24 '18 at 1:27
• @OrganicMarble That's really interesting. What did they do instead (for the OMS) when they launched with the system not functioning? – Puffin May 10 '20 at 11:30
• @Puffin IIRC they used a combination of your method 1 and 2. The OMS gauging was only updated during burns anyway so it was useless for leak detection by design. I think the biggest impact was really on the KSC guys because the OMS was loaded pre-launch to mission specific values, and it was intended to use the gauging system for that. Since it was often broken, they had to come up with an alternative. I'll see if I can find a reference on all this. – Organic Marble May 10 '20 at 12:01
• @Puffin some typical problems here: ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19950016676.pdf Note they say "failures are not uncommon and repair before the next flight is not required" And there's a very terse reference to the workarounds here: pdfs.semanticscholar.org/70b4/… – Organic Marble May 10 '20 at 12:29

A variety of systems are in use, all with flaws, basically:

1. Dead-reckoning a.k.a "book-keeping". Literally starting with a known amount at launch and then log the engine on-time and make allowances for uncertainties in thrust rise time etc. Obviously accuracy suffers from integration errors as the mission proceeds.
2. Pressure-volume-temperature. Measure the pressure/temperature of the gas in a tank and deduce from that the corresponding liquid volume. Has all sorts of physical features to keep track of such as the knowledge of propellant and gas in the system to start with, thermal expansion of the tank, vapour pressure of the liquid, location of temperature sensors. Accuracy also worsens as the mission proceeds because the resolution of the pressure transducer scales to a smaller remaining liquid volume. Various improvements such as injecting a known volume of gas mid-mission.
3. Thermal gauging. Heat the tank and watch its temperature rise. Needs a well characterised thermal model of the tank and its surroundings. In principal gets better as the tank empties as the liquid temperature excursions get larger.
4. Other methods. Flow-meters, resistance and capacitance methods do get used but are not the mainstream and are more likely to be used as a one-off mid-mission or late mission indicator, e.g. "10% remaining" (though see Organic Marble's answer on the Shuttle OMS).

Satellites

All methods 1 - 3 are in common use, especially on geostationary satellites with high yearly propellant use and critical timing of the satellite's graveyard and replacement. Methods 1 and 2 are often used in parallel.

Rocket stages

Launch vehicle stages either burn to a predetermined time or to completion. Upper stages can be extremely complex in that they can be programmed to autonomously correct for problems with lower stages but ultimately it will simply use all the propellant. For this reason I believe method 1 is the most common though it wouldn't surprise me if flow meters (4. Other methods) get used too.

Crewed missions

The shuttle with the interesting answer by Organic Marble is, I believe, relatively unusual. I believe each shuttle mission was planned to rules about allowances and margins, as also presumably is Soyuz/Progress. The notion of the general purpose spacecraft with an unspecified mission, in the same sense as filling up a car fuel tank, is still in the future though the mission profiles for all of the ISS related vehicles appears to have to change in response to events. I'd be interested to read what other methods are used.

We can use light refraction angel from liquid surface of fuel. Assumption is that the space ship is having constant velocity..... Liquid fuel always settle to the opposite side of tank (which will be tank bottom) w.r.t moving direction.

• No, constant velocity does not push the liquid down, it will still float. – Prakhar Jun 17 '19 at 4:59
• Velocity is not constant for an elliptical orbit, but for both circular and elliptical orbits there is zero gravity. Fluids in a tank do not settle in zero gravity. Acceleration is needed to settle the liquid. – Uwe Jun 18 '19 at 12:36